Deep Quaternion Networks

TL;DR

This paper introduces deep quaternion networks, extending deep learning into hyper-complex numbers, demonstrating improved convergence and efficiency on image classification and segmentation tasks.

Contribution

It develops the theoretical foundation and architecture components for deep quaternion networks, including quaternion convolutions, weight initialization, and batch-normalization algorithms.

Findings

Quaternion networks converge faster than real and complex networks.

Quaternion networks use fewer parameters for similar or better performance.

Significant improvements observed in segmentation tasks.

Abstract

The field of deep learning has seen significant advancement in recent years. However, much of the existing work has been focused on real-valued numbers. Recent work has shown that a deep learning system using the complex numbers can be deeper for a fixed parameter budget compared to its real-valued counterpart. In this work, we explore the benefits of generalizing one step further into the hyper-complex numbers, quaternions specifically, and provide the architecture components needed to build deep quaternion networks. We develop the theoretical basis by reviewing quaternion convolutions, developing a novel quaternion weight initialization scheme, and developing novel algorithms for quaternion batch-normalization. These pieces are tested in a classification model by end-to-end training on the CIFAR-10 and CIFAR-100 data sets and a segmentation model by end-to-end training on the KITTI Road Segmentation data set. These quaternion networks show improved convergence compared to real-valued and complex-valued networks, especially on the segmentation task, while having fewer parameters